The comb signal and its Fourier transform

The comb signal and its Fourier transform

In this paper, we study the aperiodic comb signal from the point of view of the Fourier Transform. The comb is very important in the theory of ideal sampling. The knowledge of its properties is crucial for the establishment of suitable interpolation schemes. Here, we present sufficient conditions so that the Fourier Transform of an aperiodic comb is an aperiodic comb. We use this result to prop...

Signal Reconstruction From The Modulus of its Fourier Transform

The problem of signal reconstruction from the magnitude of its Fourier transform arises in many applications where the wave phase is apparently lost or impractical to measure. One example of such an application that has attracted a substantial number of researchers in recent years is Coherent Diffraction Imaging (CDI). CDI is a “lens-less” technique for 2D and 3D nano-objects reconstruction wit...

Fourier Transform – Signal Processing

Signal recognition: Fourier transform vs. Cosine transform

A new feature representation approach, the simultaneous usage of the real and imaginary Fourier components with taking into account the covariance between these components, was compared with the Cosine transform approach for Gaussian recognition. 2003 Elsevier B.V. All rights reserved.

The Fast Fourier Transform and Its Applications

The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers. A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate. An analysis of the error due to discrete sampling ove...